For each orientation the Fe film was slightly strained along the \(x\) 
[GaN(0001)] direction according to its CSL as discussed above. There
is also a lattice mismatch in the \(y\) 
[GaN\((\overline{1}\overline{1}20)\) )] direction because the Fe lattice
constant and GaN \(a\)  lattice parameter differ by nearly 12%. This
mismatch was accommodated by a single CSL, common to all orientations,
containing eight unit cells of Fe and seven of GaN. The GaN substrate
was represented by a slab of four atomic layers with fixed in-plane
equilibrium lattice parameters and a passivating bottom layer.
Total energies and forces were calculated within the PBE generalized-gradient approximation
[1]} to DFT
using projector-augmented-wave potentials as implemented in vasp [2]}, [3]}.
All Fe and GaN atomic positions were fully relaxed except the bottom
GaN layer. For each Fe film orientation the formation energy depends
strongly on the choice of Fe-GaN interface registry. We systematically
varied the registry over a grid in both \(x\)  and \(y\)  to locate the
global energy minimum for each orientation. The plane-wave cutoff for
all calculations was 400 eV.
